Integral Geometry and Valuations (Advanced Courses in Mathematics - CRM Barcelona) - Tapa blanda

Libro 15 de 35: Advanced Courses in Mathematics - CRM Barcelona

Alesker, Semyon; Fu, Joseph H.G.

 
9783034808736: Integral Geometry and Valuations (Advanced Courses in Mathematics - CRM Barcelona)
Tapa blanda
ISBN 10: 3034808739 ISBN 13: 9783034808736
Editorial: Springer Basel, 2014

Sinopsis

In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, provides an introduction to the theory of convex valuations with emphasis on recent developments. In particular, it presents the new structures on the space of valuations discovered after Alesker's irreducibility theorem. The newly developed theory of valuations on manifolds is also described. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló. The approach is new and based on the notions and tools presented in the first part. This original viewpoint not only enlightens the classical integral geometry of euclidean space, but it also allows the computation of kinematic formulas in other geometries, such as hermitian spaces. The book will appeal to graduate students and interested researchers from related fields including convex, stochastic, and differential geometry. ​

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De la contraportada

Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances.

The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds.

In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces.

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Editorial
Springer Basel
Año de publicación
2014
Idioma
Inglés
ISBN 10 
3034808739
ISBN 13 
9783034808736
Encuadernación
Tapa blanda
Número de páginas
112
Editor
Gallego Eduardo, Solanes Gil
Contacto del fabricante
no disponible
Persona responsable
no disponible